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TMF, 2003, Volume 137, Number 3, Pages 393–407 (Mi tmf280)  

This article is cited in 6 scientific papers (total in 6 papers)

Monodromy Approach to the Scaling Limits in Isomonodromy Systems

A. A. Kapaev

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: The isomonodromy deformation method is applied to the scaling limits in the linear $(N\times N)$ matrix equations with rational coefficients to obtain the deformation equations for the algebraic curves that describe the local behavior of the reduced versions for the relevant isomonodromy deformation equations. The approach is illustrated by the study of the algebraic curve associated with the $n$-large asymptotics in the sequence of the biorthogonal polynomials with cubic potentials.

Keywords: scaling limits, isomonodromic deformations, WKB method, spectral curve, modulation equations

DOI: https://doi.org/10.4213/tmf280

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English version:
Theoretical and Mathematical Physics, 2003, 137:3, 1691–1702

Bibliographic databases:


Citation: A. A. Kapaev, “Monodromy Approach to the Scaling Limits in Isomonodromy Systems”, TMF, 137:3 (2003), 393–407; Theoret. and Math. Phys., 137:3 (2003), 1691–1702

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Kapaev AA, “Quasi-linear Stokes phenomenon for the Painlevé first equation”, Journal of Physics A-Mathematical and General, 37:46 (2004), 11149–11167  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. Bertola, M, “Commuting difference operators, spinor bundles and the asymptotics of orthogonal polynomials with respect to varying complex weights”, Advances in Mathematics, 220:1 (2009), 154  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Masoero D., “Poles of integrale tritronquee and anharmonic oscillators. Asymptotic localization from WKB analysis”, Nonlinearity, 23:10 (2010), 2501–2507  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    4. Buckingham R.J., Miller P.D., “Large-Degree Asymptotics of Rational Painlevé-II Functions: Noncritical Behaviour”, Nonlinearity, 27:10 (2014), 2489–2577  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    5. Dubrovin B., Kapaev A., “On An Isomonodromy Deformation Equation Without the Painlevé Property”, Russ. J. Math. Phys., 21:1 (2014), 9–35  crossref  mathscinet  zmath  isi  scopus  scopus
    6. Christian Klein, Nikola Stoilov, “Numerical Approach to Painlevé Transcendents on Unbounded Domains”, SIGMA, 14 (2018), 068, 10 pp.  mathnet  crossref
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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